Description Usage Arguments Value References Examples
Matches the expected losses of a tower of reinsurance layers using a piecewise Pareto severity
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  PiecewisePareto_Match_Layer_Losses(
Attachment_Points,
Expected_Layer_Losses,
Unlimited_Layers = FALSE,
Frequencies = NULL,
FQ_at_lowest_AttPt = NULL,
FQ_at_highest_AttPt = NULL,
TotalLoss_Frequencies = NULL,
minimize_ratios = TRUE,
Use_unlimited_Layer_for_FQ = TRUE,
truncation = NULL,
truncation_type = "lp",
dispersion = 1,
tolerance = 1e10,
alpha_max = 100,
merge_tolerance = 1e06,
RoL_tolerance = 1e06
)

Attachment_Points 
Numeric vector. Vector containing the attachment points of consecutive layers in increasing order 
Expected_Layer_Losses 
Numeric vector. Vector containing the expected losses of layers xs the attachment points. 
Unlimited_Layers 
Logical. If 
Frequencies 
Numeric vector. Expected frequencies excess the attachment points. The vector may contain NAs. If 
FQ_at_lowest_AttPt 
Numerical. Expected frequency excess 
FQ_at_highest_AttPt 
Numerical. Expected frequency excess 
TotalLoss_Frequencies 
Numeric vector. 
minimize_ratios 
Logical. If 
Use_unlimited_Layer_for_FQ 
Logical. Only relevant if no frequency is provided for the highest attachment point by the user. If 
truncation 
Numeric. If 
truncation_type 
Character. If 
dispersion 
Numerical. Dispersion of the claim count distribution in the resulting PPP_Model. 
tolerance 
Numeric. Numerical tolerance. 
alpha_max 
Numerical. Maximum alpha to be used for the matching. 
merge_tolerance 
Numerical. Consecutive Pareto pieces are merged if the alphas deviate by less than merge_tolerance. 
RoL_tolerance 
Numerical. Consecutive layers are merged if RoL decreases less than factor 
A PPP_Model object that contains the information about a collective model with a Panjer distributed claim count and a Piecewise Pareto distributed severity. The object contains the following elements:
FQ
Numerical. Frequency in excess of the lowest threshold of the piecewise Pareto distribution
t
Numeric vector. Vector containing the thresholds for the piecewise Pareto distribution
alpha
Numeric vector. Vector containing the Pareto alphas of the piecewise Pareto distribution
truncation
Numerical. If truncation
is not NULL
and truncation > max(t)
, then the distribution is truncated at truncation
.
truncation_type
Character. If truncation_type = "wd"
then the whole distribution is truncated. If truncation_type = "lp"
then a truncated Pareto is used for the last piece.
dispersion
Numerical. Dispersion of the Panjer distribution (i.e. variance to mean ratio).
Status
Numerical indicator: 0 = success, 1 = some information has been ignored, 2 = no solution found
Comment
Character. Information on whether the fit was successful
Riegel, U. (2018) Matching tower information with piecewise Pareto. European Actuarial Journal 8(2): 437–460
1 2 3 4 5 6 7 8  AP < Example1_AP
EL < Example1_EL
PiecewisePareto_Match_Layer_Losses(AP, EL)
EL_unlimited < rev(cumsum(rev(Example1_EL)))
PiecewisePareto_Match_Layer_Losses(AP, EL_unlimited, Unlimited_Layers = TRUE)
PiecewisePareto_Match_Layer_Losses(AP, EL, FQ_at_lowest_AttPt = 0.5)
Example1_FQ < c(0.3, 0.15, 0.08, 0.02, 0.005)
PiecewisePareto_Match_Layer_Losses(AP, EL, Frequencies = Example1_FQ)

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